A car moves with a constant tangential acceleration `w_tau=0.62m//s^2` along a horizontal surface circumscribing a circle of wheels of the car and the surface is `k=0.20`. What distance will the car ride without sliding if at the initial moment of time its velocity is equal to zero?

Explanation

As initial velocity is zero thus
`v^2=2w_ts` (1)
As `w_tgt0` the speed of the car increases with time or distance. Till the moment, sliding starts, the static friction provides the required centripetal acceleration to the car.
Thus `f r =mw`, but `f r lekmg`
So, `w^2lek^2g^2` or, `w_t^2+v^2/Rlek^2g^2`
or, `v^2le(k^2g^2-w_t^2)R`
Hence `v_(max)=sqrt((k^2g^2-w_t^2)R)`
so, from Eqn. (1), the sought distance `s=(v_(max)^2)/(2w_t)=1/2sqrt(((kg)/(w_t))^2-1)=60m`.